Rue et al. (2009) proposed a method for approximate Bayesian inference for latent Gaussian models called integrated nested Laplace approximation (INLA) [1]}. Latent Gaussian models are a subset of the class of Bayesian additive models with a structured additive predictor. Suppose \(y_i\)  is the response variable with distribution function in the exponential family, and with mean \(\mu _i\)  which is linked to an additive predictor \(\eta _i\)  through a link function \(g(.)\) , i.e. \(g(\mu _i)=\eta _i\) , and possibly other parameters say \(\mathbf {\theta }_2\) . The general form of \(\eta _i\)  is
\(\eta _i = \alpha + \sum _{j=1}^{n_f}f^{(j)}(u_{ij}) + \sum _{k=1}^{n_{\beta }}\beta _k z_{ik} + \epsilon _i.\) 
